Trajectory Planning Algorithms Research Articles

Jerk limited continuous tool path generation for flexible systems in non-cartesian coordinate systems

Inspired by computer numerical control (CNC) technology and drastic changes in the world of electronics and microcontrollers, the idea of using non-cartesian coordinate system for CNC machines became a topic of interest. Non-cartesian coordinate systems provide freedom of movement in systems with large working spaces where high dimensional accuracy is not a prime concern. Applications of such systems can be found in murals, where a painting is applied to a large wall of any arbitrary build material. In the present paper, a new design was introduced to automate the process of drawing murals on large surfaces. The proposed mechanism utilized chain and sprocket to overcome the size limitations of traditionally available x-y tables. In addition to that, the developed mechanism does not utilize the common robust structures used in the conventional CNC systems and the tool motion is created using flexible arms that are not heavily constrained. The effect of systems unwanted vibration has been eliminated using continuous trajectory and kinematic profiles. Parametric curve interpolation algorithms for trajectory planning were implemented to increase the flexibility of drawing complex curves. Parametric curves such as B-spline and non-uniform rational B-spline (NURBS) were employed to generate a jerk limited trajectory for motion control and extraction of kinematic profiles. Such trajectory constrains the jerk of the system and guarantees a smooth motion free of feed-rate fluctuations. Compared to other methods available for extracting the kinematic profiles, jerk limited method decreases the travel time and trajectory error. Ultimately, motion commands were produced by using kinematic profiles and the second order Taylor interpolator. STM32746ZG card was used as the main processor and two stepper motors controlled by a Bit Pattern interpolation algorithm were utilized to drive the proposed mechanism. The input pulses of stepper motors were stored as binary bits and transmitted to drivers in real-time. The feedback was also evaluated by two rotary encoders, placed at the end of the motors’ shafts. Encoder data were acquired and transmitted using a TCP/IP protocol to guarantee zero data loss during the transmission.

An improved whale optimization algorithm for UAV swarm trajectory planning

For the problem of trajectory planning in the small-scale unmanned aerial vehicle (UAV) swarms, classical intelligent algorithms and newly emerged bio-inspired algorithms often suffer from being trapped in local optima, leading to suboptimal solutions. Moreover, these algorithms fail to ensure optimal solutions and convergence speed in high-speed dynamic UAV networking scenarios. In response to these challenges, this paper proposes an Improved Whale Optimization Algorithm (IWOA) that considers the global perspective. To address the issue of initial solution diversity, an opposition-based learning method is introduced by constructing a reverse population, enhancing the diversity of the initial population. To overcome the problem of the algorithm getting trapped in local optima, random convergence factors, and end-point random neighborhood perturbations are incorporated to accelerate the global convergence speed of the IWOA and prevent it from getting stuck in local optima. Additionally, a grid digital elevation model is employed when constructing the experimental environment model, considering various physical constraints of the UAV swarm. This ensures that the simulation validation of the IWOA algorithm is closer to real-world scenarios. Simulation results indicate that, compared to commonly used algorithms, the IWOA can generate more optimal trajectories for drone swarm planning under constraints resembling real-world scenarios. It exhibits better performance in trajectory evaluation, convergence speed, and stability, thereby meeting the requirements of trajectory planning for small-scale UAV swarms. The proposed IWOA enhances UAV swarm coordination and efficiency, significantly impacting real-world applications in various fields.

Research on Trajectory Planning and Tracking Algorithm of Crawler Paver

The implementation of unmanned intelligent construction on the concrete surfaces of an airport effectively improves construction accuracy and reduces personnel investment. On the basis of three known common tracked vehicle dynamics models, reference trajectory planning and trajectory tracking controller algorithms need to be designed. In this paper, based on the driving characteristics of the tracked vehicle and the requirements of the stepping trajectory, a quartic polynomial trajectory planning algorithm was selected with the stability of the curve as a whole and the end point as the optimization goal, combining the tracked vehicle dynamics model, collision constraints, start–stop constraints and other boundary conditions. The objective function of trajectory planning was designed to effectively plan the reference trajectory of the tracked vehicle’s step-by-step travel. In order to realize accurate trajectory tracking control, a nonlinear model predictive controller with transverse-longitudinal integrated control was designed. To improve the real-time performance of the controller, a linear model predictive controller with horizontal and longitudinal decoupling was designed. MATLAB 2023A and CoppeliaSim V4.5.1 were used to co-simulate the two controller models. The experimental results show that the advantages and disadvantages of the tracked vehicle dynamics model and controller design are verified.

Enhancing Adaptability and Autonomy in Cooperative Selective Compliance Assembly Robot Arm Robots: Implementation of Coordination and Rapidly Exploring Random Tree Algorithms for Safe and Efficient Manipulation Tasks

In this study, a cooperative robotic system comprising two Selective Compliance Assembly Robot Arm (SCARA) robots was developed and simulated. An algorithm was proposed for the coordination of robots in cooperative tasks, along with a Rapidly exploring Random Tree (RRT) path planner for obstacle avoidance. The proposed system proved effective in transferring objects between robots and in handling various scenarios of variable complexity without collisions. The implementation of advanced trajectory planning and coordination algorithms significantly improves the adaptability and autonomy of robotic systems, allowing robots to predict and react to the movements of their counterparts and changes in the environment in real time. This capability is crucial for maintaining a safe and efficient work environment. The importance of synchronization and effective communication between robots is highlighted to avoid collisions and optimize trajectories and cycle times. All tests were conducted in virtual environments, allowing for the evaluation and refinement of the performance of the robots’ performance under controlled conditions. The positive results obtained in the simulations suggest that the system is well suited for future practical implementation in industrial and manufacturing applications, such as chemical handling, collaborative welding, quality inspection, among others. These findings underscore the potential of the cooperative SCARA system to improve the efficiency and safety in industrial applications using advanced algorithms and control techniques, establishing a solid foundation for future research and development in the field of cooperative robotics.

A Survey of Autonomous Vehicle Behaviors: Trajectory Planning Algorithms, Sensed Collision Risks, and User Expectations.

Autonomous vehicles are rapidly advancing and have the potential to revolutionize transportation in the future. This paper primarily focuses on vehicle motion trajectory planning algorithms, examining the methods for estimating collision risks based on sensed environmental information and approaches for achieving user-aligned trajectory planning results. It investigates the different categories of planning algorithms within the scope of local trajectory planning applications for autonomous driving, discussing and differentiating their properties in detail through a review of the recent studies. The risk estimation methods are classified and introduced based on their descriptions of the sensed collision risks in traffic environments and their integration with trajectory planning algorithms. Additionally, various user experience-oriented methods, which utilize human data to enhance the trajectory planning performance and generate human-like trajectories, are explored. The paper provides comparative analyses of these algorithms and methods from different perspectives, revealing the interconnections between these topics. The current challenges and future prospects of the trajectory planning tasks in autonomous vehicles are also discussed.

A Deep Reinforcement Learning Algorithm for Trajectory Planning of Swarm UAV Fulfilling Wildfire Reconnaissance

Wildfires have long been one of the critical environmental disasters that require a careful monitoring system. An intelligent system has the potential to both prevent/extinguish the fire and deliver urgent requirements postfire. In recent years, unmanned aerial vehicles (UAVs), with the ability to detect missions in high-risk areas, have been gaining increasing interest, particularly in forest fire monitoring. Taking a large-scale area involved in a fire into consideration, a single UAV is often insufficient to accomplish the task of covering the whole disaster zone. This poses the challenge of multi-UAVs optimum path planning with a key focus on limitations such as energy constraints and connectivity. To narrow down this issue, this paper proposes a deep reinforcement learning-based trajectory planning approach for multi-UAVs that permits UAVs to extract the required information within the disaster area on time. A target area is partitioned into several identical subareas in terms of size to enable UAVs to perform their patrol duties over the subareas. This subarea-based arrangement converts the issue of trajectory planning into allowing UAVs to frequently visit each subarea. Each subarea is initiated with a risk level by creating a fire risk map optimizing the UAV patrol route more precisely. Through a set of simulations conducted with a real trace of the dataset, the performance outcomes confirmed the superiority of the proposed idea.

Trajectory planning for AGV based on the improved artificial potential field- A* algorithm

Abstract There are many redundant nodes and inflection points in the path planned by the traditional A* algorithm, leading to the inefficient trajectory planning of the Automatic Guided Vehicle(AGV) in the multi-static obstacles environment. The artificial potential field algorithm suffers from the problem of unreachable objectives and falling into optimal local value. This article studies the trajectory optimization of AGVs to improve the trajectory planning algorithm's iteration efficiency and shorten the trajectory's total length. This article establishes the forward kinematic and Unified Robot Description Format(URDF) model of the AGV and proposes the Artificial Potential Field-A*(APF-A*) algorithm for trajectory planning. The search cost and the number of turns are effectively optimized. The article simulates the APF-A* algorithm, the results are compared with the trajectory before optimization, and the optimized time is 60% less than that before optimization. The experimental platform of AGV trajectory planning is built, and the algorithm verification experiment of AGV trajectory planning is carried out. The experimental results show that the algorithm studied in this article achieves path smoothing and trajectory length optimization.

Trajectory planning and simulation of upper limb rehabilitation robot based on NSGA2

In order to increase the stability and comfort of hemiplegic rehabilitation training, this paper integrates B-spline curves with a non-dominated sorting genetic algorithm (NSGA2) for trajectory planning of a 5-DOF upper limb exoskeleton rehabilitation robot, the structural characteristics of the robot are analyzed. Subsequently, the forward kinematics equation is derived by the D-H method, and its correctness is verified by Adams simulation. Subsequently, the robot workspace is calculated, and the outcomes show that it satisfies the patient’s demand for activity. Finally, the trajectory curve is constructed using the 5th-order B-splines. Under kinematic constraints, the NAGA2 is used to discover the ideal time interval sequence for time, impact and energy, and then complete the trajectory planning. The simulation findings demonstrate the suggested trajectory planning method produces continuous, smooth, and high-performance motion trajectories, providing good rehabilitation training for patients.

DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor

To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance.

Research on two stage obstacle-avoidance trajectory planning and trajectory tracking control in curves

The existing obstacle-avoidance trajectory planning and trajectory tracking control algorithms have limitations such as long-time consumption, high failure rate in dynamic traffic environments, and insufficient trajectory tracking accuracy in curved roads. Based on the above problems, this paper designs a two stage obstacle-avoidance trajectory planner based on nonlinear optimization theory. In first stage Part-NLP, only considering the safety obstacle avoidance, a point mass model and linearization constraints are established to quickly solve the initial trajectory. In the second stage Full-NLP, considering smooth soft constraints comprehensively, the initial trajectory is optimized by establishing driving corridors and a lightweight iterative framework. In control module, this paper selects a linear quadratic form lateral trajectory tracking controller, and the parameters were optimized through the carnivorous plant algorithm. The joint simulation results show that in dynamic traffic environment of curved roads, the two stage planner proposed can accurately plan safe and smooth obstacle avoidance trajectories, and there is a significant reduction in time consumption compared to traditional NLP algorithms. The control strategy can accurately track the planned trajectories, with lateral error controlled within plus or minus 0.1 m, heading error controlled within plus or minus 0.15 rad, speed tracking error controlled within plus or minus 0.15 m/s, and vehicle yaw angle error controlled within plus or minus 0.04 rad; the hardware-in-loop test results indicate that the controller can achieve real-time and accurate trajectory tracking.

Trajectory Planning and Singularity Avoidance Algorithm for Robotic Arm Obstacle Avoidance Based on an Improved Fast Marching Tree

The quest for efficient and safe trajectory planning in robotic manipulation poses significant challenges, particularly in complex obstacle environments where the risk of encountering singularities and obstacles is high. Addressing this critical issue, our study presents a novel enhancement of the Fast Marching Tree (FMT) algorithm, ingeniously designed to navigate the complex terrain of Cartesian space with an unprecedented level of finesse. At the heart of our approach lies a sophisticated two-stage path point sampling strategy, ingeniously coupled with a singularity avoidance mechanism that leverages geometric perception to assess and mitigate the risk of encountering problematic configurations. This innovative method not only facilitates seamless obstacle navigation but also adeptly circumvents the perilous zones of singularity, ensuring a smooth and uninterrupted path for the robotic arm. To further refine the trajectory, we incorporate a quasi-uniform cubic B-spline curve, optimizing the path for both efficiency and smoothness. Our comprehensive simulation experiments underscore the superiority of our algorithm, showcasing its ability to consistently achieve shorter, more efficient paths while steadfastly avoiding obstacles and singularities. The practical applicability of our method is further corroborated through successful implementation in real-world robotic arm trajectory planning scenarios, highlighting its potential to revolutionize the field with its robustness and adaptability.

基于EMSDBO算法农业植保无人机三维航迹多目标优化研究

Both cruising ability and safety should be considered in the 3D inspection path planning of agricultural unmanned aerial vehicles (UAVs). Specific to a complex working environment, the 3D inspection environment of agricultural UAVs was simulated through terrain modeling and threat modeling. First, the dynamic constraints of flight approaching rate and response time were added to the threat cost, and the 3D mission space model and flight path cost function were constructed considering the influence of UAVs’ turning performance. Second, the offset estimation strategy, variable spiral search strategy, quasi-reverse learning strategy and dimension-by-dimension mutation strategy were introduced into the dung beetle optimizer (DBO) algorithm to improve the global optimization ability and convergence rate of the algorithm. By establishing a three-dimensional trajectory planning model for unmanned aerial vehicles, the trajectory planning is transformed into a multi-objective function optimization problem, and an improved algorithm is used to solve the three-dimensional trajectory planning of unmanned aerial vehicles. The fitness is evaluated by considering the objective function of trajectory cost, terrain cost, and danger level, and the trajectory planning is iteratively optimized. The results indicate that the proposed improved dung beetle algorithm for trajectory planning has lower overall cost and stability in adapting to different complex terrain environments.

Optimization of Clustering and Trajectory for Minimizing Age of Information in Unmanned Aerial Vehicle-Assisted Mobile Edge Computing Network.

With the development of the Internet of Things (IoT) technology, massive amounts of sensor data in applications such as fire monitoring need to be transmitted to edge servers for timely processing. However, there is an energy-hole phenomenon in transmitting data only through terrestrial multi-hop networks. In this study, we focus on the data collection task in an unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) network, where a UAV is deployed as the mobile data collector for the ground sensor nodes (SNs) to ensure high information freshness. Meanwhile, the UAV is equipped with an edge server for data caching. We first establish a rigorous mathematical model in which the age of information (AoI) is used as a measure of information freshness, related to both the data collection time and the UAV's flight time. Then a mixed-integer non-convex optimization problem is formulated to minimize the peak AoI of the collected data. To solve the problem efficiently, we propose an iterative two-step algorithm named the AoI-minimized association and trajectory planning (AoI-MATP) algorithm. In each iteration, the optimal SN-collection point (CP) associations and CP locations for the parameter ε are first obtained by the affinity propagation clustering algorithm. The optimal UAV trajectory is found using an improved elite genetic algorithm. Simulation results show that based on the optimized ε, the AoI-MATP algorithm can achieve a balance between data collection time and flight time, reducing the peak AoI of the collected data.

Nonlinear model predictive control for trajectory-planning and tracking based on tilting technology to achieve vehicle obstacle avoidance

ABSTRACT High-speed autonomous vehicles can effectively improve the performance of obstacle-avoidance trajectory-planning and tracking control through integration with existing electronic control systems. However, relatively little research has been conducted in this field. This paper proposes a novel methodology of obstacle-avoidance trajectory-planning and tracking control based on active front-wheel steering integrated with tilting technology that can tilt the vehicle body toward the inside of the curve via active suspension when turning. The controller is designed using hierarchical control, in which the upper layer uses the point-mass vehicle model to design the trajectory-planning algorithm based on model predictive control. The lower layer uses the nonlinear vehicle model to design obstacle-avoidance tracking nonlinear model predictive control based on active steering integrated with tilt control. Then, the constrained nonlinear model predictive control problem is transformed into a constrained nonlinear programming problem, which is solved by sequential quadratic programming. Finally, simulations were performed using the CarSim/Simulink co-simulation platform. Two other hierarchical obstacle-avoidance tracking nonlinear model predictive controllers were designed as comparison objects. The simulation results show that the planning trajectory of the proposed integrated controller is closest to the obstacle. This controller effectively improves the vehicle obstacle-avoidance trajectory-tracking performance, handling stability, and maneuverability.

A Joint Optimization Algorithm for Trajectory Planning and Resource Allocation of Vehicle Mobile Base Stations for On-Demand Coverage Networks

In today’s urban hotspot regions, service traffic exhibits dynamic variations in both time and location. Traditional fixed macro base stations (FMBSs) are unable to meet these dynamic demands due to their fixed coverage and capacity. Therefore, this paper introduces a novel algorithm for the joint optimization of the placement of terrestrial vehicle-mounted mobile micro base stations (mBSs), the correlation of service clusters (SCs) with mBSs, and resource assignments. The objective is to maximize the matching degree between network capacity and service demands while adhering to constraints related to the power, coverage, and bandwidth of mBSs, as well as the data rate required for the services. Additionally, we investigate the mobility of the mBSs towards the SCs in the spatiotemporal changing service demand network and obtain optimal trajectories for the mBSs. We begin by formulating the problem of maximizing the matching degree by analyzing the capacity provided by the base stations and the network service demand. Subsequently, we derive solutions to the optimization problem using our algorithm. The simulation results demonstrate that the proposed algorithm can effectively meet the capacity demand of dynamically changing hotspot regions and achieve on-demand, resilient coverage of hotspot regions in the network.

Geometric field model of driver’s perceived risk for safe and human-like trajectory planning

Autonomous driving systems must provide safe, predictable, and consistent behaviors across diverse scenarios to enhance user experience. The geometric driver risk field (GDRF) method is proposed for human-like, interpretable, and fast risk estimations. The method models the driver’s subjectively perceived risk with fields formed by sets of geometric shapes. Unlike current safety measures adopted in trajectory planning algorithms, the proposed method aligns with driver risk perception properties. It provides risk estimations based on probable future vehicle states and the risk consequences at different locations. Compared with existing potential field methods for risk estimations, the mathematical form of the method has a high calculation efficiency while keeping the ability to model the details of the risk information. Influences of different obstacle types, multiple regions with different risk levels, and the relative motions between vehicles are modeled in a unified manner. The graph-search and optimization trajectory planning algorithms with a hierarchy framework are also designed to attain desired risk objectives in the planned trajectories. The framework mitigates the possible suboptimality problems in previous hierarchy trajectory planning algorithms. The proposed GDRF method and planning algorithms are examined in driving scenarios with different traffic states and road geometries. Results showed that the proposed risk estimation method outperforms previous risk-oriented potential field methods by more human-like and safer trajectories with evidence from existing studies and safety measures like time headway (THW), time to collision (TTC), and time to lane crossing (TLC). It also provides more consistent behaviors while maintaining a short computation time. The integration of the proposed risk estimation method and trajectory planning algorithms holds great potential for improving the safety and user experience of autonomous driving systems in real-world scenarios.

Cone Slalom With Automated Sports Car–Trajectory Planning Algorithm

Cone Slalom With Automated Sports Car–Trajectory Planning Algorithm

Deep Imitation Learning for Optimal Trajectory Planning and Initial Condition Optimization for an Unstable Dynamic System

In this article, an innovative offline deep imitation learning algorithm for optimal trajectory planning is proposed. While many state‐of‐the‐art works achieved optimal trajectory planning, their systems were stable or quasistable, and their approaches rarely optimized the system's initial conditions (ICs). Here, a new unstable dynamic system task called “internal sliding object stabilization control” is proposed, modeled, and solved by deep imitation learning. Given the system's ICs, the neural networks (NNs) can imitate the iterative linear quadratic regulator (iLQR), generate optimal trajectories, and compute faster. A proportional–integral–derivative (PID) controller is used to track the unstable trajectories. Leveraging on the gradients of NNs, it can optimize the system's ICs, avoid obstacles stepwise, and ensure the worst bounds of NNs for safety. Subsequently, thorough simulations are conducted, including comparing the iLQR and PID controllers in the task, optimizing the system's different ICs by gradient descent, and finding the worst bound of the performance by gradient ascent. Results show that the proposed algorithm achieves considerably improved performance. Finally, experiments are conducted with a real manipulator to compare the proposed structure with the original iLQR. Results indicate that the proposed algorithm resembles the iLQR well. Program code and experiment results are in https://github.com/DanielYamChen/ISOSC.git.

Application of Game Refinement Theory to Automated Driving

In recent years, assisted driving and self-driving have captured the imagination of manufacturers, designers, technology providers, and the general public with the expectation of a sustainable, safer, and intelligent mobility in the near future. Self-driving or assisted driving vehicles are complex systems that integrate environmental perception, intelligent planning and decision-making, tracking, and control. With the increasing intelligence of vehicles, personalized design is an inevitable trend. A design that is in line with the driver’s personality can bring a better driving experience to the driver. Thus, classifying driving types while driving in a self-driving environment may play an important role in the construction of trajectory planning algorithms. This paper uses the motion-in-mind model from game refinement theory to model driver behavior. Further, a classification of the model parameters into three categories helped in distinguishing cautious, aggressive, and average drivers. The results showed that the self-driving environment can be successfully modeled as a game and adaptation to match the riders’ driving skills may improve satisfaction.

Trajectory planning of large redundant manipulator considering kinematic constraints and energy efficiency

AbstractFor the large redundant manipulator, due to its long working distance and large mass, the number of links (i.e., manipulator’s arms) that can be driven to move simultaneously is limited. Otherwise, the control accuracy and motion stability of the manipulator will deteriorate. Focusing on that, a weighted Newton iteration (WNI) algorithm for trajectory planning of the manipulator is firstly proposed, where the motion of the manipulator joints is controlled by a weight matrix, which is constant and related to each link’s energy consumption. To dynamically adjust the weight matrix according to kinematic constraints and acquire better energy efficiency, an adaptive WNI (AWNI) algorithm is further proposed. In AWNI, the weight matrix is adjusted in real-time during the planning process, with considerations of the kinematic constraints and the energy consumption of the manipulator. The switch of the links between the working state and the non-working state is made through the weight matrix to achieve flexible control of the manipulator motion. Two evaluation functions are established to validate the effectiveness of AWNI in energy saving and motion stability control. Taking a 6 degrees of freedom (DOF) manipulator as an example, simulation experiments on trajectory planning are carried out and the results show the effectiveness of the proposed AWNI algorithm.